After 100%, the extension saves the file to the default download folder. Try downloading small files with the built-in download and this extension. If the problem still exists, open an issue here.
There are buttons to resume broken tasks and copy the URL in the panel.
You tried feeding JDownloader and didn't like it. That doesn't leave many options, as feeding an outside download manager is really the only alternative to the limited internal download managers (That are much worse now because of the limitations of Web Extensions).
With that said, I went looking one day and ended up on Multithreaded Download Manager . It does the trick and it's open source as well.